TSTP Solution File: SYN712-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN712-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:35:48 EDT 2023
% Result : Unsatisfiable 2.64s 0.74s
% Output : Proof 2.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN712-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 21:00:22 EDT 2023
% 0.14/0.36 % CPUTime :
% 2.64/0.74 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.64/0.74
% 2.64/0.74 % SZS status Unsatisfiable
% 2.64/0.74
% 2.64/0.75 % SZS output start Proof
% 2.64/0.75 Take the following subset of the input axioms:
% 2.64/0.75 fof(not_p62_67, negated_conjecture, ~p62(f5(c64, f8(f11(f13(c65, c66), c67), c68)), c69)).
% 2.64/0.75 fof(p2_28, negated_conjecture, ![X44]: p2(X44, X44)).
% 2.64/0.75 fof(p32_20, negated_conjecture, ![X92]: p32(X92, X92)).
% 2.64/0.75 fof(p3_104, negated_conjecture, ![X24, X25, X26, X27, X28]: p3(f16(f19(f21(c70, f8(f11(f13(c65, X24), X25), X26)), X27), X28), f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, X24), X25), X26), X27), X28)), f43(f45(f47(f49(f51(c75, X24), X25), X26), X27), X28)), f53(f55(f57(f59(f61(c76, X24), X25), X26), X27), X28)))).
% 2.64/0.75 fof(p4_82, negated_conjecture, ![X123, X124, X125, X126]: (p4(f5(X123, X124), f5(X125, X126)) | (~p2(X123, X125) | ~p3(X124, X126)))).
% 2.64/0.75 fof(p62_100, negated_conjecture, p62(f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72)), c69)).
% 2.64/0.75 fof(p62_69, negated_conjecture, ![X199, X200, X202, X201]: (p62(X199, X200) | (~p4(X202, X199) | (~p62(X202, X201) | ~p32(X201, X200))))).
% 2.64/0.75 fof(p62_97, negated_conjecture, ![X203, X204, X205, X206]: (p62(X203, X204) | ~p62(f5(c64, f8(f11(f13(c65, X203), X205), X206)), X204))).
% 2.64/0.75 fof(p62_98, negated_conjecture, ![X203_2, X204_2, X205_2, X206_2]: (p62(f5(c64, f8(f11(f13(c65, X203_2), X205_2), X206_2)), X204_2) | ~p62(X203_2, X204_2))).
% 2.64/0.75 fof(p62_99, negated_conjecture, ![X29, X24_2, X25_2, X26_2, X27_2, X28_2]: (p62(X24_2, X29) | ~p62(f23(f25(f27(f29(f31(c74, X24_2), X25_2), X26_2), X27_2), X28_2), X29))).
% 2.64/0.75
% 2.64/0.75 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.64/0.75 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.64/0.75 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.64/0.75 fresh(y, y, x1...xn) = u
% 2.64/0.75 C => fresh(s, t, x1...xn) = v
% 2.64/0.75 where fresh is a fresh function symbol and x1..xn are the free
% 2.64/0.75 variables of u and v.
% 2.64/0.75 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.64/0.75 input problem has no model of domain size 1).
% 2.64/0.75
% 2.64/0.75 The encoding turns the above axioms into the following unit equations and goals:
% 2.64/0.75
% 2.64/0.75 Axiom 1 (p32_20): p32(X, X) = true2.
% 2.64/0.75 Axiom 2 (p2_28): p2(X, X) = true2.
% 2.64/0.75 Axiom 3 (p62_69): fresh129(X, X, Y, Z) = true2.
% 2.64/0.75 Axiom 4 (p62_97): fresh16(X, X, Y, Z) = true2.
% 2.64/0.75 Axiom 5 (p62_99): fresh14(X, X, Y, Z) = true2.
% 2.64/0.75 Axiom 6 (p62_69): fresh17(X, X, Y, Z, W) = p62(Y, Z).
% 2.64/0.75 Axiom 7 (p62_69): fresh128(X, X, Y, Z, W, V) = fresh129(p4(W, Y), true2, Y, Z).
% 2.64/0.75 Axiom 8 (p4_82): fresh41(X, X, Y, Z, W, V) = p4(f5(Y, Z), f5(W, V)).
% 2.64/0.75 Axiom 9 (p4_82): fresh40(X, X, Y, Z, W, V) = true2.
% 2.64/0.75 Axiom 10 (p62_98): fresh15(X, X, Y, Z, W, V) = true2.
% 2.64/0.75 Axiom 11 (p62_69): fresh128(p62(X, Y), true2, Z, W, X, Y) = fresh17(p32(Y, W), true2, Z, W, X).
% 2.64/0.75 Axiom 12 (p4_82): fresh41(p2(X, Y), true2, X, Z, Y, W) = fresh40(p3(Z, W), true2, X, Z, Y, W).
% 2.64/0.75 Axiom 13 (p62_98): fresh15(p62(X, Y), true2, X, Z, W, Y) = p62(f5(c64, f8(f11(f13(c65, X), Z), W)), Y).
% 2.64/0.75 Axiom 14 (p62_97): fresh16(p62(f5(c64, f8(f11(f13(c65, X), Y), Z)), W), true2, X, W) = p62(X, W).
% 2.64/0.75 Axiom 15 (p62_100): p62(f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72)), c69) = true2.
% 2.64/0.75 Axiom 16 (p62_99): fresh14(p62(f23(f25(f27(f29(f31(c74, X), Y), Z), W), V), U), true2, X, U) = p62(X, U).
% 2.64/0.75 Axiom 17 (p3_104): p3(f16(f19(f21(c70, f8(f11(f13(c65, X), Y), Z)), W), V), f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, X), Y), Z), W), V)), f43(f45(f47(f49(f51(c75, X), Y), Z), W), V)), f53(f55(f57(f59(f61(c76, X), Y), Z), W), V))) = true2.
% 2.64/0.75
% 2.64/0.75 Goal 1 (not_p62_67): p62(f5(c64, f8(f11(f13(c65, c66), c67), c68)), c69) = true2.
% 2.64/0.75 Proof:
% 2.64/0.75 p62(f5(c64, f8(f11(f13(c65, c66), c67), c68)), c69)
% 2.64/0.75 = { by axiom 13 (p62_98) R->L }
% 2.64/0.75 fresh15(p62(c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.75 = { by axiom 16 (p62_99) R->L }
% 2.64/0.75 fresh15(fresh14(p62(f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.75 = { by axiom 14 (p62_97) R->L }
% 2.64/0.75 fresh15(fresh14(fresh16(p62(f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.75 = { by axiom 6 (p62_69) R->L }
% 2.64/0.75 fresh15(fresh14(fresh16(fresh17(true2, true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69, f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72))), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 1 (p32_20) R->L }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh17(p32(c69, c69), true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69, f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72))), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 11 (p62_69) R->L }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh128(p62(f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72)), c69), true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69, f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72)), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 15 (p62_100) }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh128(true2, true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69, f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72)), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 7 (p62_69) }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh129(p4(f5(c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72)), f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72)))), true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 8 (p4_82) R->L }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh129(fresh41(true2, true2, c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72), c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 2 (p2_28) R->L }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh129(fresh41(p2(c64, c64), true2, c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72), c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 12 (p4_82) }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh129(fresh40(p3(f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72), f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), true2, c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72), c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 17 (p3_104) }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh129(fresh40(true2, true2, c64, f16(f19(f21(c70, f8(f11(f13(c65, c66), c67), c68)), c71), c72), c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 9 (p4_82) }
% 2.64/0.76 fresh15(fresh14(fresh16(fresh129(true2, true2, f5(c64, f8(f11(f13(c65, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72)), f43(f45(f47(f49(f51(c75, c66), c67), c68), c71), c72)), f53(f55(f57(f59(f61(c76, c66), c67), c68), c71), c72))), c69), true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 3 (p62_69) }
% 2.64/0.76 fresh15(fresh14(fresh16(true2, true2, f23(f25(f27(f29(f31(c74, c66), c67), c68), c71), c72), c69), true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 4 (p62_97) }
% 2.64/0.76 fresh15(fresh14(true2, true2, c66, c69), true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 5 (p62_99) }
% 2.64/0.76 fresh15(true2, true2, c66, c67, c68, c69)
% 2.64/0.76 = { by axiom 10 (p62_98) }
% 2.64/0.76 true2
% 2.64/0.76 % SZS output end Proof
% 2.64/0.76
% 2.64/0.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------